Question

Identify the 12th term of the geometric sequence in which a2 = −6 and a6 = −96

Answer 1

Answer:

The 12th term of the geometric sequence is: -6144

Step-by-step explanation:

We need to find r, and we have some information:

$a_2:-6$ y $a_6=-96$

$a_2:a_6=r^4$ because (6-2=4)

$-6:-96 =r^4\\r^4=16$ because -96/-6=16

$r=\sqrt[4]{16}\\r=2$

The equation to find the n term is:

$a_n=-3*2^n^-^1$

Now, we need to find $a_1_2$

$a_1_2=-3*2^1^2^-^1\\a_1_2=-3*2^1^1\\a_1_2=-3*2048\\a_1_2=-6144$

Answer 2

$a_2=-6;\ a_6=-96\\\\a_6:a_2=r^4\\\\r^4=-96:(-6)\\\\r^4=16\\\\r=\sqrt[4]{16}\\\\r=2\\\\a_{12}=a_6r^6\\\\a_{12}=-96\cdot2^6=-96\cdot64=-6,144$